Spherical formation tracking of non-holonomic vehicles in three-dimensional space

This paper studies spherical coordinated formation control problem of three-dimensional (3D) non-holonomic vehicles forming the zonal formation and tracking the desired circle on a target sphere under the bidirectional communication topology. Differing from spherical self motions of particles via the control input projected to the direction of normal vector, spherical meridian and spherical parallel separately for sphere tracking, circle tracking on the sphere and zonal formation, each vehicle's pitch and yaw velocities and surge acceleration here are combined together to achieve spherical formation tracking motion. The design is based on our previous geometric expansion and the Lyaponov method. The performance of the proposed control law is showed by numerical simulations.